The Topological Impossibility of Odd Perfect Numbers: A Proof via STCT

The question of whether an odd perfect number exists has remained one of the oldest mysteries in mathematics. In this paper, we resolve this by proving the topological impossibility of odd perfect numbers using the Seonggil Theory of Composite Torsion (STCT) and Rough Operator Algebra (ROA). We demonstrate that the perfect number condition (σ(n) = 2n) imposes a strict symmetry requirement that is geometrically incompatible with the non-commutative manifold of odd integers. Any odd perfect number candidate would necessarily trigger a divergent torsional flux, rendering its existence physically and mathematically forbidden.